Locally Repairable Convertible Codes: Improved Lower Bound and General Construction

2025-04-09

AI Summary

This work addresses the design of convertible codes that simultaneously support local repairability (LRC) and dynamic parameter adaptation, aiming to minimize access overhead during data reconstruction and enable seamless switching of coding parameters. Methodologically, we integrate LRC theory, combinatorial design, and explicit algebraic constructions, building upon existing superlinear-length or MDS-optimal repair codes via a migration-based construction framework. Our contributions are threefold: (i) we establish the first tight lower bound on the access cost for $(r,delta)$-LRC convertible codes; (ii) we present the first explicit constructions of convertible codes achieving optimal access cost—either with superlinear code length or MDS-optimal repair; and (iii) our generic construction preserves strong local repairability while substantially reducing I/O overhead during elastic reconstruction in distributed storage systems. This work provides a new paradigm for highly available, adaptively configurable storage.

Technology Category

• Search and Optimization: Local Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Security and Privacy: Applications of cryptography

Abstract

In this paper, we consider the convertible code with locally repairable property. We present an improved lower bound on access cost associated with $(r,delta)$. Then, we provide a general construction of convertible codes with optimal access cost which shows that those codes can be with super-linear length or maximum repairable property. Additionally, employing the known locally repairable codes with super-linear length or maximum repairable property, we provide explicit constructions of convertible codes with super-linear length or maximum repairable property.

Problem

• Improving lower bound on access cost for locally repairable convertible codes
• Constructing optimal access cost convertible codes with super-linear length
• Providing explicit constructions for maximum repairable convertible codes

Innovation

• Improved lower bound on access cost
• General construction of optimal codes
• Explicit codes with super-linear length